多维匹配
Multi-Dimensional Matching
浏览论文内容
中文总结 AI 辅助
我们提出一种基于特征谱投影的多维匹配机制，实现高效计算并保证纳什社会福利最优，在AI购物应用中验证其诊断能力。
中文摘要 AI 辅助
我们研究了一种匹配机制，其中代理和对象由特征而非完整排序来描述。单一的谱投影将问题简化为一维排序，可在O(N log N)时间内计算。我们证明，在去尺度化的特征和偏好上，我们的算法在投影空间内获得精确的纳什社会福利（NSW）最优解，具有无条件功利福利保证和有条件的NSW保证。所提出的机制对外生噪声稳定，但不是策略证明的；我们提供了一个明确的有利可图的误报。在一个人工智能购物应用中，诊断正确预测了成功和失败案例。一项100实例的稳健性研究证实了这些发现。
英文摘要
We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.
